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A371284
Number of integer partitions of n whose distinct parts form the set of divisors of some number.
6
0, 1, 1, 2, 3, 4, 5, 8, 9, 11, 12, 16, 18, 23, 25, 32, 36, 42, 47, 57, 62, 73, 81, 96, 106, 123, 132, 154, 168, 190, 207, 240, 259, 293, 317, 359, 388, 434, 469, 529, 574, 635, 688, 768, 826, 915, 987, 1093, 1181, 1302, 1397, 1540, 1662, 1818, 1959, 2149, 2309
OFFSET
0,4
COMMENTS
The Heinz numbers of these partitions are given by A371288.
EXAMPLE
The partition y = (10,5,5,5,2,2,1) has distinct parts {1,2,5,10}, which form the set of divisors of 10, so y is counted under a(30).
The a(1) = 1 through a(8) = 9 partitions:
(1) (11) (21) (31) (221) (51) (331) (71)
(111) (211) (311) (2211) (421) (3311)
(1111) (2111) (3111) (511) (4211)
(11111) (21111) (2221) (5111)
(111111) (22111) (22211)
(31111) (221111)
(211111) (311111)
(1111111) (2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Union[#]==Divisors[Max[#]]&]], {n, 0, 30}]
CROSSREFS
The strict case is A054973, ranks A371283 (unsorted version A275700).
These partitions have ranks A371288.
A000005 counts divisors, row-lengths of A027750.
A000041 counts integer partitions, strict A000009.
A008284 counts partitions by length, strict A008289.
Sequence in context: A161389 A266118 A287802 * A214207 A302497 A044051
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 22 2024
STATUS
approved